The Nanoelectronic Modeling Tool NEMO 5: Capabilities, Validation, and

Application to Sb-Heterostructures

Sebastian Steiger1, Michael Povolotskyi

1, Hong-Hyun Park

1, Tillmann Kubis

1, Ganesh Hegde

1,

Benjamin Haley1, Mark Rodwell

2 and Gerhard Klimeck

1,3

1Network for Computational Nanotechnology, Purdue University, West Lafayette IN 47906, USA

2University of California, Santa Barbara, CA 93106, USA

3Email: gekco@purdue.edu. Phone: (765) 494-9212

Introduction

Modeling and simulation take an important role in the exploration and design optimization of novel devices.

As the downscaling of electronic devices continues, the description of interfaces, randomness, and disorder on

an atomistic level gains importance and continuum descriptions lose their validity. Often a full-band

description of the electronic structure is needed to model the interaction of different valleys and

nonparabolicity effects. NEMO 5 [1] is a modeling tool that addresses these issues and is able to provide

insight into a broad range of devices. It unifies the capabilities of prior projects: multiscale approaches to

quantum transport in planar structures in NEMO-1D [2], multimillion-atom simulations of strain and electronic

structure in NEMO-3D [3] and NEMO-3D-Peta [4], and quantum transport in nonplanar structures in OMEN

[5]. NEMO 5 aims at becoming a community code whose structure, implementation, resource requirements

and license allow experimental and theoretical researchers in academia and industry alike to use and extend the

tool.

Capabilities and Validation

NEMO 5 currently handles pseudomorphic nanostructures composed of diamond, zincblende, simple-cubic,

wurtzite, graphene and rhombohedral (trigonal) crystals. It is able to compute strain in large structures using

an enhanced valence force field model [6] (Fig. 1). The same physical model can be used to find phonon

spectra (Fig. 2). These capabilities have been validated against various literature results [7].

Electronic structure calculations are done using the empirical tight-binding method [8] using a variety of

nearest-neighbor models ranging from an effective mass description to the 20-band sp3d

5s

* model. Bulk band

structures for most IV and III-V materials were validated against literature results. Band diagrams of

nanostructures were shown to coincide with independently developed codes. The influence of strain can be

treated using the formulation of Ref. 9 or an enhanced version [10]. Quantum Dot Lab [11], an educational

version of an effective mass solver with interactive 3D wavefunction and absorption visualization that uses

NEMO 5 as an engine, is available online at nanoHUB.org without the need for any installation.

Selfconsistent Schroedinger-Poisson calculations can be performed using a multiscale approach where the

density can be based on a mixture of quantum and semiclassical models. This enables the simulation of larger

structures where the computationally intensive solution of the Schrödinger equation is restricted to the central

parts. A 1D version of this capability can be accessed online [12] through nanoHUB.org (Fig. 3). This type of

simulation was also validated with independently developed code.

Quantum transport through nanostructures can be computed using two approaches. For ballistic, coherent

calculations an open-boundary wavefunction method is preferred [13] (Fig. 4). These calculations have been

validated against literature [14] and prior developed code [5]. Electron-phonon scattering can be included in a

deformation-potential description [15] using the NEGF formalism [14].

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Application: Sb heterostructures

As an example application we present band structure calculations of two antimonide-based heterostructures.

[111]-Sb heterostructures were recently proposed as high-current HEMT candidates [16]. The relative

proximity of the -, X- and L-valleys, their coupling through translational symmetry breaking as well as the

large anisotropy of carrier masses make the validity of a standard effective mass approach questionable. The

calculations in this section were performed using an sp3d

5s

* tight-binding model including spin-orbit coupling.

The parameter sets were determined using genetic-algorithm fitting against literature values for conduction and

valence band edges and masses. The fitting process of the parameters including strain effects is still ongoing

and the final parameter sets will be published elsewhere [17]. The lattice mismatch of 0.6% (GaSb/AlSb) and

1.3% (InAs/AlSb) is neglected for this work.

In Fig. 5 a triple-QW GaSb-AlSb structure grown along [111] is displayed where the barriers between the

wells consist of a single Al-atom. With a lattice constant of 0.61nm, a single [111]-AlSb monolayer has a

thickness of about 0.35nm. Although the -valley in bulk GaSb is slightly (30meV) lower than the L-valley,

the enormous difference of the effective masses in the confinement direction (0.04 vs. 1.3) pushes the confined

-state far above the confined L-state. The high confinement masses also allow for ultrathin barrier layers,

enabling exquisite electrostatic control and multiple conduction channels. Yet the in-plane effective masses of

the 6 lowest bands remain small such that a fast device can be expected. A series of simulations with well and

barrier thicknesses varying between 1 and 3 ML (Table 1) reveals that the in-plane effective masses remain at

around 0.09-0.10, close to the bulk value. The masses were obtained by fitting the lowest QW subband within

0.15/a of the minimum, as transport in high-current devices occurs above the band edge. A carrier density of

1e13cm-2

at a temperature of 300K positions the Fermilevel EF about 70-90meV above the subband edge E0L

assuming six parabolic bands. Conversely, EF–Ec~0.2eV is able to accommodate n2D~2-3e13cm-2

. As Table 1

illustrates, the separation of higher bands with larger in-plane masses exceeds 0.2eV for most settings.

A second simulation example is the [100]-AlSb/InAs/GaSb/InAs/AlSb single quantum well depicted in Fig.

6a. This heterostructure features no-common-atom interfaces which are preferably of the type In-Sb [18]. The

question of tight-binding parameter mixing for the interface bonds has not yet been fully answered. In this

work InAs parameters were taken for the In-Sb interface. Especially the split-off valence subband depends on

this choice as there are large differences in spin-orbit coupling. The resulting band structure (Fig. 6b) shows

large band warping in the valence bands. As expected, the k=0 eigenfunctions (Fig. 6c) of the conduction band

are mostly located in the InAs layers whereas the valence band states are confined to the GaSb layer.

This paper introduces our latest NEMO 5 tool kit to the advanced research community and highlights

capabilities relevant to very recent DRC-discussed results [16].

[1] S. Steiger et al., manuscript in preparation.

[2] R. Lake et al., J. Appl. Phys. 81, 7845 (1997)

[3] G. Klimeck et al., IEEE Trans. El. Dev. 54, 2090 (2007)

[4] S. Lee et al., Proc. IWCE 13, 1 (2009)

[5] G. Klimeck and M. Luisier, Proc. IEDM, 1 (2008)

[6] Z. Sui et al., Phys. Rev. B 48, 17938 (1993)

[7] A. Paul et al., J. Comp. Electron. 9, 160 (2010)

[8] G. Klimeck et al., CMES 3, 601 (2002)

[9] T. Boykin et al., Phys. Rev. B 66, 125207 (2002)

[10] T. Boykin et al., Phys. Rev. B 81, 125202 (2010)

[11] DOI: 10254/nanohub-r450.10

[12] DOI: 10254/nanohub-r5203.15

[13] M. Luisier et al., Phys. Rev. B 74, 205323 (2006)

[14] S. Datta, Superlatt. Microstruct. 28, 253 (2000)

[15] S. Jin et al., J. Appl. Phys. 99, 123719 (2006)

[16] M. Rodwell et al., Proc. DRC, 149 (2010)

[17] G. Hegde et al., manuscript in preparation

[18] H. Kroemer, Phys. E 20, 196 (2004)

[19] B. Dorner et al., J. Phys.:Cond. Mat. 2, 1475 (1990)

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Fig. 1: Strain relaxation in a dome-shaped InAs quantum

dot embedded in (100nm)3 GaAs consisting of 44 million

atoms. The dot is 20 nm wide and 5 nm high, consisting of

about 38000 atoms. Shown is the magnitude of the

displacement vector. Inset: Strain component zz.

Fig. 2: Bulk phonon dispersions of GaAs computed using the

Keating model (blue – dashed) and an extended VFF model with

augmented Coulomb interaction (red - solid). Also shown are

experimental measurements [19] (black crosses).

Fig. 3: 1D Heterostructure Design tool on

nanoHUB.org. Top: Structure definition screen.

Bottom: Computed electron states and energies.

Fig. 4: Transport through an ultrathin-body transistor at Vds=0.5V. From

top to bottom: Id-Vg curve, schematic of the structure, electrostatic

potential and electron density at Vg=0.9V.

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1 ML

(0.35nm)

2 ML

(0.7nm)

3ML

(1.05nm)

1 ML

m*=0.086

EL=248

E=223

m*=0.088

EL=50

E=177

m*=0.094

EL=48

E=152

2 ML

m*=0.105

EL=35

E=224

m*=0.102

EL=13

E=270

m*=0.102

EL=37

E=277

3 ML

m*=0.095

EL=58

E=240

m*=0.098

EL=12

E=263

m*=0.100

EL=9

E=277

Fig. 5: [111]-GaSb/AlSb triple-QW structure (2 ML wells, 1ML

barriers) and in-plane band diagram

Table 1: [111]-GaSb/AlSb triple-QW dependence of

m*, the splitting EL and the distance E=min(E0X

,E1L)-E0L (meV) on well and barrier thicknesses

Fig. 6: AlSb/InAs/GaSb/InAs/AlSb double-QW. a) Atomistic structure. b) In-plane band dispersion. c) k=0 eigenstate

wavefunctions for selected energies (average between anion and cation positions).

GaSb

AlSb

AlSb

b) c)

a)

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